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Abstract Let $$T$$ be a satellite knot, link, or spatial graph in a 3-manifold $$M$$ that is either $S^3$ or a lens space. Let $$\b_0$$ and $$\b_1$$ denote genus 0 and genus 1 bridge number, respectively. Suppose that $$T$$ has a companion knot $$K$$ (necessarily not the unknot) and wrapping number $$\omega$$ with respect to $$K$$. When $$K$$ is not a torus knot, we show that $$\b_1(T)\geq \omega \b_1(K)$$. There are previously known counter-examples if $$K$$ is a torus knot. Along the way, we generalize and give a new proof of Schubert's result that $$\b_0(T) \geq \omega \b_0(K)$$. We also prove versions of the theorem applicable to when $$T$$ is a "lensed satellite" and when there is a torus separating components of $$T$$. 

Effective file system testing relies on coverage to detect bugs and enhance reliability. We analyzed real file system bugs and found a weak correlation between code coverage, the most commonly used metric, and test effectiveness; many bugs were in covered code but remained undetected. Our study also showed that covering diverse file system inputs and outputs—system call arguments and return values—can be key to detecting the majority of observed bugs. We present input coverage and output coverage as new metrics for evaluating and improving file system testing, and have developed the IOCov framework for computing these metrics. Unlike existing system call tracers, IOCov computes coverage using only the calls relevant to testing, excluding unrelated ones that should not be counted. To demonstrate IOCov’s utility, we used it to extend the existing testing tool CrashMonkey into CM-IOCov, which achieves broader input coverage and more thorough detection of crash consistency bugs. Our experimental evaluation shows that IOCov com- putes input and output coverage accurately with minimal overhead. IOCov is applicable to different types of file system testing and can provide insights for improvement as well as identify untested cases based on coverage results. Moreover, the bugs found exclusively by CM-IOCov are 2.1 and 12.9 times more than those found exclusively by CrashMonkey on the 6.12 and 5.6 kernels, respectively, demonstrating the effectiveness of the IOCov-based coverage approach. 

Information from frequency bands in biomedical time series provides useful summaries of the observed signal. Many existing methods consider summaries of the time series obtained over a few well-known, pre-defined frequency bands of interest. However, there is a dearth of data-driven methods for identifying frequency bands that optimally summarize frequency-domain information in the time series. A new method to identify partition points in the frequency space of a multivariate locally stationary time series is proposed. These partition points signify changes across frequencies in the time-varying behavior of the signal and provide frequency band summary measures that best preserve nonstationary dynamics of the observed series. An $$L_2$$-norm based discrepancy measure that finds differences in the time-varying spectral density matrix is constructed, and its asymptotic properties are derived. New nonparametric bootstrap tests are also provided to identify significant frequency partition points and to identify components and cross-components of the spectral matrix exhibiting changes over frequencies. Finite-sample performance of the proposed method is illustrated via simulations. The proposed method is used to develop optimal frequency band summary measures for characterizing time-varying behavior in resting-state electroencephalography time series, as well as identifying components and cross-components associated with each frequency partition point. 

Abstract South American summer monsoon (SASM) strength tracks insolation on orbital timescales, linking global climate and continental hydrology. However, whether local water availability also responds to global climate forcings is unclear. Here, we present water balance records from Lake Junín, an Andean lake within the SASM domain. Local water balance and SASM strength is inferred from triple oxygen isotopes of lake carbonates during two interglacial periods (Marine Isotope Stage (MIS) 15, 621–563 ka; the Holocene, 11.7–0 ka). We find SASM strength and water balance both follow the precession‐pacing of local summer insolation, with the driest conditions occurring at Lake Junín under weakened SASM conditions (and vice versa). Further, the largest variations occurred during MIS 15, when insolation was more variable than the Holocene. These results suggest that global climate influences South American hydrology on both the local and continental scales, with implications for tropical water resources, the atmospheric greenhouse effect, and ecosystem dynamics. 

Although rates of fluvial incision across the Colorado Plateau are known reasonably well, rate variability through time and its controlling processes are still poorly understood. We used boulder armored benches from the Teasdale-Torrey lowlands reach of the Fremont River in the northwestern Colorado Plateau (Utah, USA) as temporal markers to determine regional incision rates and explore controls on rate variability. Bench gravels are sourced from Tertiary volcanic rocks capping nearby Boulder and Thousand Lakes Mountains. The sedimentology of bench deposits suggests that most form from mass movement with later fluvial reworking. Volcanic boulders are tougher than the local sedimentary bedrock, which promotes boulder armoring and topographic inversion. Thirty-seven boulder cosmogenic 3He exposure ages from 11 different benches range from >600 ka to ca. 100 ka. Soil carbonate stages from two benches are in good agreement with surface exposure ages. Averaged Fremont River and tributary incision rates determined from bench exposure ages are 32% faster for tributaries off of Thousand Lakes Mountain (0.41 m/k.y.) than tributaries off of Boulder Mountain (0.28 m/k.y.). This difference in incision rate may be due to Laramideage structures limiting incision for the tributaries that drain Boulder Mountain and extensive Pleistocene ice caps on Boulder Mountain creating a wider and thicker boulder armor slowing incision. 

Abstract Sulfate-proton co-transporters (SULTRs) mediate sulfate uptake, transport, storage, and assimilation in plants. The SULTR family has historically been classified into four groups (SULTR1-SULTR4), with well-characterized roles for SULTR groups 1, 2, and 4. However, the functions of the large and diverse SULTR3 group remain poorly understood. Here, we present an updated phylogenetic analysis of SULTRs across angiosperms, including multiple early-divergent lineages. Our results suggest that the enigmatic SULTR3 group comprises four distinct subfamilies that predate the emergence of angiosperms, providing a basis for reclassifying the SULTR family into seven subfamilies. This expanded classification is supported by subfamily-specific gene structures and amino acid substitutions in the substrate-binding pocket. Structural modeling identified three serine residues uniquely lining the substrate-binding pocket of SULTR3.4, enabling three hydrogen bonds with the phosphate ion. The data support the proposed neofunctionalization of this subfamily for phosphate allocation within vascular tissues. Transcriptome analysis of Populus tremula × alba revealed divergent tissue expression preferences among SULTR subfamilies and between genome duplicates. We observed partitioned expression in vascular tissues among the four SULTR3 subfamilies, with PtaSULTR3.4a and PtaSULTR3.2a preferentially expressed in primary and secondary xylem, respectively. Gene coexpression analysis revealed coordinated expression of PtaSULTR3.4a with genes involved in phosphate starvation responses and nutrient transport, consistent with a potential role in phosphate homeostasis. In contrast, PtaSULTR3.2a was strongly coexpressed with lignification and one-carbon metabolism genes and their upstream transcription regulators. PtaSULTR3.2a belongs to a eudicot-specific branch of the SULTR3.1 subfamily found only in perennial species, suggesting a specialized role in lignifying tissues. Together, our findings provide a refined phylogenetic framework for the SULTR family and suggest that the expanded SULTR3 subfamilies have undergone neofunctionalization during the evolution of vascular and perennial plants. 

Abstract Analysis of ion-kinetic instabilities in solar wind plasmas is crucial for understanding energetics and dynamics throughout the heliosphere, as evident from spacecraft observations of complex ion velocity distribution functions (VDFs) and ubiquitous ion-scale kinetic waves. In this work, we explore machine learning (ML) and deep learning (DL) classification models to identify unstable cases of ion VDFs driving kinetic waves. Using 34 hybrid particle-in-cell simulations of kinetic protons andα-particles initialized using plasma parameters derived from solar wind (SW) observations, we prepare a data set of nearly 1600 VDFs representing stable/unstable cases and associated plasma and wave properties. We compare feature-based classifiers applied to VDF moments, such as support vector machine and random forest (RF), with DL convolutional neural networks (CNNs) applied directly to VDFs as images in the gyrotropic velocity plane. The best-performing classifier, RF, has an accuracy of 0.96 ± 0.01, and a true skill score of 0.89 ± 0.03, with the majority of missed predictions made near stability thresholds. We study how the variations of the temporal derivative thresholds of anisotropies and magnetic energies, and sampling strategies for simulation runs, affect classification. CNN-based models have the highest accuracy of 0.88 ± 0.18 among all considered if evaluated on the runs entirely not used during the model training. The addition of theE_⊥power spectrum as an input for the ML models leads to the improvement of instability analysis for some cases. The results demonstrate the potential of ML and DL for the detection of ion-scale kinetic instabilities using spacecraft observations of SW and magnetospheric plasmas. 

We use thin position of Heegaard splittings to give a new proof of Haken's Lemma that a Heegaard surface of a reducible manifold is reducible and of Scharlemann's ``Strong Haken Theorem'': a Heegaard surface for a 3-manifold may be isotoped to intersect a given collection of essential spheres and discs in a single loop each. We also give a reformulation of Casson and Gordon's theorem on weakly reducible Heegaard splittings, showing that they exhibit additional structure with respect to certain incompressible surfaces. This article could also serve as an introduction to the theory of generalized Heegaard surfaces and it includes a careful study of their behaviour under amalgamation. 

Abstract Recent observations of the solar wind ions by the SPAN-I instruments on board the Parker Solar Probe (PSP) spacecraft at solar perihelia (Encounters) 4 and closer find ample evidence of complex anisotropic non-Maxwellian velocity distributions that consist of core, beam, and “hammerhead” (i.e., anisotropic beam) populations. The proton core populations are anisotropic, withT_⊥/T_∥ > 1, and the beams have super-Alfvénic speed relative to the core (we provide an example from Encounter 17). Theα-particle population shows similar features to the protons. These unstable velocity distribution functions (VDFs) are associated with enhanced, right-hand (RH) and left-hand (LH) polarized ion-scale kinetic wave activity, detected by the FIELDS instrument. Motivated by PSP observations, we employ nonlinear hybrid models to investigate the evolution of the anisotropic hot-beam VDFs and model the growth and the nonlinear stage of ion kinetic instabilities in several linearly unstable cases. The models are initialized with ion VDFs motivated by the observational parameters. We find rapidly growing (in terms of proton gyroperiods) combined ion-cyclotron and magnetosonic instabilities, which produce LH and RH ion-scale wave spectra, respectively. The modeled ion VDFs in the nonlinear stage of the evolution are qualitatively in agreement with PSP observations of the anisotropic core and “hammerhead” velocity distributions, quantifying the effect of the ion kinetic instabilities on wind plasma heating close to the Sun. We conclude that the wave–particle interactions play an important role in the energy transfer between the magnetic energy (waves) and random particle motion, leading to anisotropic solar wind plasma heating.